Analyse du comportement vibratoire des plaques fissurées par la X-FEM

Dans cet article, la méthode des éléments finis étendue (X-FEM) est utilisée pour décrire le comportement vibratoire des plaques présentant une discontinuité à différentes positions. La théorie utilisée est celle de Mindlin, où les effets de l'inertie de rotation et des déformations en cisaillement transverse sont pris en considération. Deux types d'éléments sont testés dans la discrétisation par éléments finis à savoir, élément quadratique à 4 nœuds et élément quadratique à 9 nœuds. La technique d'itération en sous espace est ensuite utilisée pour la résolution du problème aux valeurs propres. Différentes applications sont considérées, à savoir : cas des plaques avec fissure centrale et plaques avec fissure au bord. Les résultats obtenus en termes de fréquences propres et en fonction de la longueur de la fissure sont satisfaisants comparativement à ceux disponibles dans la littératur

Dynamic analysis of cracked plates by the extended finite element method (X-FEM)

Dynamic analysis of isotropic and composite plates containing through cracks are analyzed. Since regular finite element needs not only re-meshing at discontinuities, but also requires high mesh density at singularities, a search for an efficient numerical method is thus suitable. Because of its efficiency in not requiring re-meshing at singularities, the extended finite element method (X-FEM) is widely used in fracture mechanics problems. However and according to our knowledge, the XFEM has not yet been used in the dynamic analysis of cracked structures, subject of the present work. The analysis of dynamic behavior of isotropic and composite plates having a through crack located at various positions is conducted. At first, conventional FEM without any discontinuity is carried out; then, enrichment of nodal elements containing cracks is added to the FEM model. Various plates configurations with different kinds of boundary conditions and with different crack lengths and locations are considered. Primary observations show that the frequency of all the modes of vibration decreases with the increase of the crack length. This physical effect is more pronounced for some specific modes as it also depends on the nature of the singularit

Les polynomes semi-classiques de classe zero et de classe un

CNRS T 58868 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueSIGLEFRFranc

EFFECTS OF GEOMETRIC RATIOS AND FIBRE ORIENTATION ON THE NATURAL FREQUENCIES OF LAMINATED COMPOSITE PLATES

<p>The present investigation aims to examine the influence of geometric ratios and fibre orientation on the natural frequencies of fibre-reinforced laminated composite plates using finite element method based on Yang’s theory and his collaborators. The transverse shear and rotatory inertia effects were taken into consideration in the developed Fortran computer program. It has been shown that the use of first-order displacement field provides the same accuracy as higher-order displacement field when the number of elements representing the plate structure is increased (refined mesh). However, poor precision may appear for plates with high thickness-to-side ratio <em>h/a</em> (thickness/side length). This discrepancy limits the application of the developed theory to thick plates (<em>h/a</em>&lt;0.5). The various curves show the evolution of the dimensionless frequency (w*) <em>versus</em> fibre orientation angle (q) and illustrate the apparition of a “triple-point” phenomenon engendered by the increase of the plate aspect ratio <em>a/b</em> (length/width) for a specific value of <em>h/a</em>. This point defines the maximum natural frequency and the associated fibre orientation. Also, results show that for high and/or low aspect ratios, the triple-point phenomenon does not occur. This latter is rapidly reached for thick plates than thin plates when the plate aspect ratio<em> a/b</em> is progressively increased.</p

EFFECTS OF GEOMETRIC RATIOS AND FIBRE ORIENTATION ON THE NATURAL FREQUENCIES OF LAMINATED COMPOSITE PLATES

The present investigation aims to examine the influence of geometric ratios and fibre orientation on the natural frequencies of fibre-reinforced laminated composite plates using finite element method based on Yang’s theory and his collaborators. The transverse shear and rotatory inertia effects were taken into consideration in thedeveloped Fortran computer program. It has been shown that the use of first-order displacement field provides the same accuracy as higher-order displacement field when the number of elements representing the plate structure is increased (refined mesh).However, poor precision may appear for plates with high thickness-to-side ratio h/a (thickness/side length). This discrepancy limits the application of the developed theory to thick plates (h/a<0.5). The various curves show the evolution of the dimensionless frequency (*) versus fibre orientation angle () and illustrate the apparition of a “triple-point” phenomenon engendered by the increase of the plate aspect ratio a/b (length/width) for a specific value of h/a. This point defines the maximum naturalfrequency and the associated fibre orientation. Also, results show that for high and/or low aspect ratios, the triple-point phenomenon does not occur. This latter is rapidly reached for thick plates than thin plates when the plate aspect ratio a/b is progressively increased

Damage prediction in composite plates subjected to low velocity impact

In this investigation, fiber-reinforced composite plates subjected to low velocity impact are studied by the use of finite element analysis (FE). Mindlin’s plate theory is implemented into the FE approach in which a 9-node Lagrangian element is considered. Dynamic stress analysis is carried out by the use of a constitutive equation of composite laminates without damage. A parametric analysis shows that the increase in the percentage of the 90 plies increases the contact force implying a reduction in the rigidity of the laminate. Stresses are calculated at nine Gaussian points of each element of each interface and then averaged. At first, threshold velocities are evaluated for different stacking sequence to predict matrix crack initiation. Then, the impact induces damage at a higher impact velocity including matrix cracking is predicted by the appropriate failure criteria. The present results indicate that matrix cracking appears in the upper 90 plies with the dominance of transverse shear stres

Analyse du comportement vibratoire des plaques fissurées par la X-FEM

Colloque avec actes et comité de lecture. Internationale.International audienceDans cet article, la méthode des éléments finis étendue (X-FEM) est utilisée pour décrire le comportement vibratoire des plaques présentant une discontinuité à différentes positions. La théorie utilisée est celle de Mindlin, où les effets de l'inertie de rotation et des déformations en cisaillement transverse sont pris en considération. Deux types d'éléments sont testés dans la discrétisation par éléments finis à savoir, élément quadratique à 4 nœuds et élément quadratique à 9 nœuds. La technique d'itération en sous espace est ensuite utilisée pour la résolution du problème aux valeurs propres. Différentes applications sont considérées, à savoir : cas des plaques avec fissure centrale et plaques avec fissure au bord. Les résultats obtenus en termes de fréquences propres et en fonction de la longueur de la fissure sont satisfaisants comparativement à ceux disponibles dans la littératur

Perforation Analysis by Punching of Metal Sheets

In this work, a numerical study of the perforation of 6061-T6 aluminum, Titanium Ti6Al4V and stainless steel (Nitronic33) plates by a rigid flat nose punch is carried out. The Johnson-Cook model was used to define the behavior of the material constituting the plate. This homogeneous behavior was coupled with the Johnson-Cook rupture criterion to completely predict the perforation process. Initially, the present results are validated by comparing them with the results reported in the literature, including those obtained from experimental work. Thereafter, several numerical parametric analyses are performed to investigate the behavior of these metal plates depending on the maximum breaking force, the temperature in the perforated plates, the kinetic energy, the clearance on the shape of the sheared edge, and the dimensional accuracy of the plates

Prevalence of coccidian infection in rabbit farms in North Algeria

Aim: The aim of the present study was to determine the prevalence and intensity of rabbit coccidiosis (Oryctolagus cuniculus) in North Algeria. Materials and Methods: During the study, 40 rabbit farms were investigated. The farms are located in the provinces of Tizi Ouzou, Medea, and Djelfa which distributed, respectively, into three regions: East Tell Atlas Mountains, Central Tell Atlas Mountains, and High Plateaus. The number of oocyst per gram of feces (OPG) was determined by McMaster technique, and the Eimeria species were identified using morphological criteria. Results: In the farms investigated, the prevalence of coccidian infection was estimated to 90% (80.7-99.3%) in rabbits after weaning. The classification of the farms according to their parasite load allowed us to show that 37.5% of the prospective farms have an oocyst excretion between 104 and 5×104 oocysts per gram and 22.5% excrete >5×104 oocysts per gram. Excretion levels by region show that the region of East Tel Atlas Mountains ranks first with 79% of farms with a parasitic load >104 coccidians compared to the regions of Central Tel Atlas Mountains and High Plateaus. In total, eight species of Eimeria were identified from oocyst-positive samples. Mixed infections with four Eimeria species were common. E. magna is the dominant species in comparison with E. media and E. irresidua with respective frequencies of 42.5% and 17.6% and 14.9% (p<0.001). Our results showed that the farms using anticoccidial drugs for their rabbits were low (25%) and the percentage of farms with poor hygienic conditions was 65%. There was a significant association between increased oocysts excretion and control measures of coccidian infection. Conclusion: The study revealed an overall prevalence of 90% in the three Algerian regions. A strong association was observed between Eimeria infection and hygienic status and preventional chemotherapy